Derivada de tan(2x)*sec(2x)

Answer

2⋅sec(2⋅x)2cos(2⋅x)+2⋅sin(2⋅x)⋅tan(2⋅x)cos(2⋅x)2\frac{2 \cdot \mathrm{sec}\left(2 \cdot x\right)^{2}}{\mathrm{cos}\left(2 \cdot x\right)}+\frac{2 \cdot \mathrm{sin}\left(2 \cdot x\right) \cdot \mathrm{tan}\left(2 \cdot x\right)}{\mathrm{cos}\left(2 \cdot x\right)^{2}}
2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x)

Derivative of tan(2x)*sec(2x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(2⋅x)\tan(2 \cdot x)*sec⁡(2⋅x)\sec(2 \cdot x): use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
  2. Differentiate each factor and combine.
  3. Final answer: 2⋅c2 \cdot cos(2⋅x2 \cdot x)^(-1)*sec⁡(2⋅x)2\sec(2 \cdot x)^2+2⋅c2 \cdot cos(2⋅x2 \cdot x)^(-2)*sin⁡(2⋅x)\sin(2 \cdot x)*tan⁡(2⋅x)\tan(2 \cdot x)

La derivada de tan(2*x)*sec(2*x) es 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x).

Solución paso a paso instantánea para tan(2x)*sec(2x)

DerivativeTrigonometricIntermediate
Share this result
Share on X

Derivative of tan(2x)*sec(2x) = 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-tan2xsec2x

Cómo encontrar la derivada de tan(2x)*sec(2x)

Para encontrar la derivada de tan(2x)*sec(2x), usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.

Practicar Más Problemas

Derivada de 1/x
Resolver d/dx 1/x
Derivada de 1/x^2
Resolver d/dx 1/x^2
Derivada de 10^x
Resolver d/dx 10^x
Derivada de 2^x
Resolver d/dx 2^x
Derivada de 2x
Resolver d/dx 2x
Derivada de 3x^2
Resolver d/dx 3x^2
Derivada de 5x
Resolver d/dx 5x
Derivada de Abs(x)
Resolver d/dx Abs(x)
Derivada de acos(x)
Resolver d/dx acos(x)
Derivada de asin(x)
Resolver d/dx asin(x)

Frequently Asked Questions

What is the derivative of tan(2x)*sec(2x)?▼
The derivative of tan(2x)*sec(2x) is 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x).
How do you find the derivative of tan(2x)*sec(2x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x).
Why is the derivative of tan(2x)*sec(2x) equal to 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(2x)*sec(2x) yields 2*cos(2*x)^(-1)*sec(2*x)^2+2*cos(2*x)^(-2)*sin(2*x)*tan(2*x). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️